A and B working together can finish a job in d days. If A : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 15:57

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A and B working together can finish a job in d days. If A

Author Message
TAGS:

### Hide Tags

Director
Joined: 26 Feb 2006
Posts: 904
Followers: 4

Kudos [?]: 107 [0], given: 0

A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

14 Jul 2007, 17:58
7
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

77% (05:37) correct 23% (02:28) wrong based on 471 sessions

### HideShow timer Statistics

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

A. 25
B. 60
C. 15
D. 14
E. 13

[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Apr 2012, 23:35, edited 2 times in total.
Edited the question and added the OA
Senior Manager
Joined: 12 Mar 2012
Posts: 369
Concentration: Operations, Strategy
Followers: 2

Kudos [?]: 169 [5] , given: 31

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

15 Apr 2012, 17:36
5
KUDOS
Himalayan wrote:
A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25
(2) 60
(3) 15
(4) 14
(5) 13

1/(d+5) +1/(d+45)= 1/d
=> (2d+50)d = (d+5)*(d+45)
=> d^2 = 9*5*5
=> d= 15

hence option C.
_________________

Practice Practice and practice...!!

If there's a loophole in my analysis--> suggest measures to make it airtight.

Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7101

Kudos [?]: 93565 [5] , given: 10578

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

15 Apr 2012, 23:36
5
KUDOS
Expert's post
2
This post was
BOOKMARKED
Himalayan wrote:
A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25
(2) 60
(3) 15
(4) 14
(5) 13

If A works alone and completes the job, he will take d + 5 days --> the rate of A is $$\frac{1}{d+5}$$ job/day;
If B works alone and completes the job, he will take d + 45 days --> the rate of B is $$\frac{1}{d+45}$$ job/day;

Since A and B working together can finish a job in d days, then their combined rate is $$\frac{1}{d}$$ job/day;

So, $$\frac{1}{d+5}+\frac{1}{d+45}=\frac{1}{d}$$. At this point it's MUCH better to substitute the values from the answer choices rather than to solve for $$d$$.

Answer choice C fits: $$\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}$$.

_________________
Manager
Joined: 28 Aug 2012
Posts: 52
Concentration: Operations, Marketing
GMAT 1: 510 Q36 V25
GPA: 4
WE: Information Technology (Other)
Followers: 0

Kudos [?]: 125 [3] , given: 105

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

25 Dec 2012, 20:21
3
KUDOS
4
This post was
BOOKMARKED
There is always a trick to such Qs when your given A+B= x days , A= x+ something , B=x+ something .
To find X , use the formula X=$$\sqrt{ab}$$

X=$$\sqrt{5*45}$$
X= 15 days

Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2654
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 117

Kudos [?]: 1342 [1] , given: 789

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

23 Dec 2015, 05:13
1
KUDOS
Expert's post
saiesta wrote:
Bunuel wrote:
Himalayan wrote:
A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25
(2) 60
(3) 15
(4) 14
(5) 13

If A works alone and completes the job, he will take d + 5 days --> the rate of A is $$\frac{1}{d+5}$$ job/day;
If B works alone and completes the job, he will take d + 45 days --> the rate of B is $$\frac{1}{d+45}$$ job/day;

Since A and B working together can finish a job in d days, then their combined rate is $$\frac{1}{d}$$ job/day;

So, $$\frac{1}{d+5}+\frac{1}{d+45}=\frac{1}{d}$$. At this point it's MUCH better to substitute the values from the answer choices rather than to solve for $$d$$.

Answer choice C fits: $$\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}$$.

Could you please show the expanded form as to how to solve for d please? Thank you.

1 thing I would mention here as Bunuel has mentioned as well, you need to be intelligent to pick your battles in GMAT. It is not about finding the correct answer but you also need to make sure that you do not spend more time than what you should be spending.

Putting in the values in the options after you get 1/(d+5) + 1/(d+45) = 1/d , is the fastest way to solve this equation.

But for the sake of your question, look below for the solution:

1/(d+5) + 1/(d+45) = 1/d ---> $$\frac{(2d+50)}{(d+5)(d+45)} = \frac{1}{d}$$ ---> $$2d^2+50d=d^2+50d+225$$ ---> $$d^2=225$$ --->$$d = \pm 15$$, you can not have d < 0 as the number of days can only be >0.

Thus d= 15 is the only acceptable solution.

Hope this helps.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2654
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 117

Kudos [?]: 1342 [1] , given: 789

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

23 Dec 2015, 05:14
1
KUDOS
Expert's post
Manager
Joined: 12 Feb 2012
Posts: 136
Followers: 1

Kudos [?]: 48 [0], given: 28

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

15 Apr 2012, 17:29
Sorry to revisit an old post but this was a toughy! Its not a necessary condition that d be an integer.

So working together they can do the job is d days.
Let $$r_1$$ be the rate of A
Let $$r_2$$ be the rate of B

Working together their rates to do the job is
Equation1:
$$(r_1+r_2)d=1 (job)$$

A working alone can do the job by
Equation2:
$$(r_1)(d+5)=1 (job)$$

B working alone can do the job by
Equation3:
$$(r_2)(d+45)=1 (job)$$

Now set the first equation to the second equation

$$(r_1+r_2)d=1 = (r_1)(d+5)$$ solve for d to get $$d=5(r_1/r_2)$$

Now set equation1 to equation2

$$(r_1)(d+5)=1 =(r_2)(d+45)$$ solve to get $$r_1/r_2=(d+45)/(d+5)$$

Now substitute $$d=5(r_1/r_2)=5((d+45)/(d+5))$$

to get $$d(d+5)=5(d+45)$$

which leads you to $$d^2=5*45$$. Which is equal to $$d=15$$ when you square root both sides (of couse d must be positive, were talking about days here!).

Again, tough problem. If anyone has an easier method let us know.

Last edited by alphabeta1234 on 15 Apr 2012, 17:39, edited 1 time in total.
Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 235
Schools: Johnson '15
Followers: 2

Kudos [?]: 50 [0], given: 16

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

15 Apr 2012, 20:40
Himalayan wrote:
A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25
(2) 60
(3) 15
(4) 14
(5) 13

take the total work as X

so both A & B can do it in d days, A alone in d+5 and B alone in d+45

rate calculation is total rate = sum of individual rates

X/d = X/(d+5) + X/(d+45)

we can remove X, then the equation becomes as below

1/d = 1/(d+5) + 1/(d+45)

d^2 = 225

d= + or - 15

u cannot have days in negative right as it should take some time to do a task...hence 15 is the answer...

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat
_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

Satyameva Jayate - Truth alone triumphs

Senior Manager
Joined: 22 Nov 2010
Posts: 288
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)
Followers: 5

Kudos [?]: 138 [0], given: 75

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

23 Jan 2013, 22:56
1
This post was
BOOKMARKED
thinktank wrote:
There is always a trick to such Qs when your given A+B= x days , A= x+ something , B=x+ something .
To find X , use the formula X=$$\sqrt{ab}$$

X=$$\sqrt{5*45}$$
X= 15 days

What is the source of this trick? good one though.it can reduce the time to ans tremendously
_________________

YOU CAN, IF YOU THINK YOU CAN

Manager
Joined: 28 Aug 2012
Posts: 52
Concentration: Operations, Marketing
GMAT 1: 510 Q36 V25
GPA: 4
WE: Information Technology (Other)
Followers: 0

Kudos [?]: 125 [0], given: 105

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

24 Jan 2013, 00:47
I was going through this 9th grade math text book to pick up on my basics, found a number of shortcuts there
Manager
Joined: 18 Oct 2011
Posts: 90
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 69 [0], given: 0

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

24 Jan 2013, 11:16
1
This post was
BOOKMARKED
1/A = 1/(d+5)
1/B = 1/(d+45)

therefore... 1/(d+5) + 1/(d+45) = 1/d

When you do the math you end up with d^2 = 225. Therefore, d=15
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7101

Kudos [?]: 93565 [0], given: 10578

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

25 Jan 2013, 04:40
chiccufrazer1 wrote:
:shock: at bunuel..but solving for d is mathematically correct..then why is it that our answer is C

_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13522
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

17 Jun 2014, 08:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13522
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

18 Aug 2015, 08:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Manager
Joined: 23 Sep 2015
Posts: 96
Concentration: General Management, Finance
GMAT 1: 680 Q46 V38
GMAT 2: 690 Q47 V38
GPA: 3.5
Followers: 0

Kudos [?]: 14 [0], given: 213

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

08 Nov 2015, 21:40
can someone show the steps (expanded form) on how to solve for d from the formula

1/(d+5) + 1/(d+45) = 1/d

thanks
Manager
Joined: 03 Jan 2015
Posts: 91
Followers: 0

Kudos [?]: 28 [0], given: 146

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

23 Dec 2015, 05:03
Bunuel wrote:
Himalayan wrote:
A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25
(2) 60
(3) 15
(4) 14
(5) 13

If A works alone and completes the job, he will take d + 5 days --> the rate of A is $$\frac{1}{d+5}$$ job/day;
If B works alone and completes the job, he will take d + 45 days --> the rate of B is $$\frac{1}{d+45}$$ job/day;

Since A and B working together can finish a job in d days, then their combined rate is $$\frac{1}{d}$$ job/day;

So, $$\frac{1}{d+5}+\frac{1}{d+45}=\frac{1}{d}$$. At this point it's MUCH better to substitute the values from the answer choices rather than to solve for $$d$$.

Answer choice C fits: $$\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}$$.

Could you please show the expanded form as to how to solve for d please? Thank you.
Intern
Joined: 08 Feb 2015
Posts: 4
Followers: 0

Kudos [?]: 1 [0], given: 91

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

22 Jun 2016, 13:32
thinktank wrote:
There is always a trick to such Qs when your given A+B= x days , A= x+ something , B=x+ something .
To find X , use the formula X=$$\sqrt{ab}$$

X=$$\sqrt{5*45}$$
X= 15 days

Was there an explanation to this trick ? Thanks
Director
Joined: 04 Jun 2016
Posts: 656
GMAT 1: 750 Q49 V43
Followers: 50

Kudos [?]: 201 [0], given: 36

Re: A and B working together can finish a job in d days. If A [#permalink]

### Show Tags

22 Jul 2016, 09:55
Himalayan wrote:
A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

A. 25
B. 60
C. 15
D. 14
E. 13

Rate of $$A=\frac{1}{(d+5)}$$

Rate of $$B=\frac{1}{(d+45)}$$

Rate of $$A+B= \frac{1}{d}$$

Rate of $$A+B= \frac{1}{(d+45)} + \frac{1}{(d+5)}$$

$$\frac{2d+50}{(d+5)(d+45)}=\frac{1}{d}$$

$$(2d+50)d= (d+5)(d+45)$$

$$2d^2+50d=d^2+5d+45+225$$

$$2d^2+50d=d^2+50d+225$$

$$2d^2-d^2=225$$

$$d^2=225$$

$$d=\sqrt{225}$$

$$d=15$$

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016.

Re: A and B working together can finish a job in d days. If A   [#permalink] 22 Jul 2016, 09:55
Similar topics Replies Last post
Similar
Topics:
12 Five men started working on a job that was to be finished in hundred d 8 31 Aug 2014, 00:09
27 A and B together can complete one-ninth of a job in a day. 7 24 Jul 2013, 18:25
7 Bob and Alice can finish a job together in 3 hours. 4 27 Oct 2011, 13:17
76 Working together, printer A and printer B would finish the 17 01 Sep 2010, 10:12
12 Working together, printer A and printer B would finish the 7 20 Oct 2008, 02:40
Display posts from previous: Sort by